Question

A waterfall has a height of 1700 feet. A pebble is thrown upward from the top of the falls with an initial velocity of  feet per second. The height of the pebble h in feet after t seconds is given by the equation h=-16t^2+24t+1700 . How long after the pebble is thrown will it hit the​ ground?


PLEASE HELPPPPP

Answer 1

Answer:

$t = 11.085$

Step-by-step explanation:

The expression is given as:

$h=-16t^2+24t+1700$

Required

Determine how long it will hit the ground

When the pebble is on the ground, this implies that h = 0

So, we have that:

$h=-16t^2+24t+1700$ becomes

$0=-16t^2+24t+1700$

Reorder

$-16t^2+24t+1700 = 0$

Multiply through by -1

$16t^2-24t-1700 = 0$

Solve using quadratic formula $ax^2 + bx + c = 0$:

$t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a = 16$   $b = -24$    $c = -1700$

So, we have:

$t = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

$t = \frac{-(-24) \± \sqrt{(-24)^2 - 4*16*(-1700)}}{2*16}$

$t = \frac{24 \± \sqrt{576 + 108800}}{32}$

$t = \frac{24 \± \sqrt{109376}}{32}$

$t = \frac{24 \± 330.72}{32}$

$t = \frac{24 + 330.72}{32}$ or $t = \frac{24 - 330.72}{32}$

$t = \frac{354.72}{32}$ or $t = \frac{-306.72}{32}$

$t = 11.085$ or $t = -9.585$

But time can't be negative.

So: $t = 11.085$

Hence, it will take 11.085 seconds to hit the ground